Abstract

An efficient iterative algorithm is presented to solve a system of linear matrix equations , with real matrices and . By this iterative algorithm, the solvability of the system can be determined automatically. When the system is consistent, for any initial matrices and , a solution can be obtained in the absence of roundoff errors, and the least norm solution can be obtained by choosing a special kind of initial matrix. In addition, the unique optimal approximation solutions and to the given matrices and in Frobenius norm can be obtained by finding the least norm solution of a new pair of matrix equations , where , . The given numerical example demonstrates that the iterative algorithm is efficient. Especially, when the numbers of the parameter matrices are large, our algorithm is efficient as well.